返回式航天器轨道周期变率确定及预报的数值方法

对返回式航天器进行变轨控制计算时要用到平均轨道周期变率,而数值法定轨通常求解的是大气阻力系数,无法直接得到平均轨道周期变率。文章通过建立航天器精密动力学模型、数值积分器、瞬时轨道根数到平均轨道根数的转换算法和平均周期序列多项式拟合算法,提出了一种基于数值法精密轨道确定和预报计算平均轨道周期变率的数值方法。     

Dynamics of a spacecraft and normalization around Lagrangian points in the Neptune–Triton system

The problem of a spacecraft orbiting the Neptune–Triton system is presented. The new ingredients in this restricted three body problem are the Neptune oblateness and the high inclined and retrograde motion of Triton. First we present some interesting simulations showing the role played by the oblateness on a Neptune’s satellite, disturbed by Triton. We also give an extensive numerical exploration in the case when the spacecraft orbits Triton, considering Sun, Neptune and its planetary oblateness as disturbers. In the plane a × I (a = semi-major axis, I = inclination), we give a plot of the stable regions where the massless body can survive for thousand of years. Retrograde and direct orbits were considered and as usual, the region of stability is much more significant for the case of direct orbit of the spacecraft (Triton’s orbit is retrograde). Next we explore the dynamics in a vicinity of the Lagrangian points. The Birkhoff normalization is constructed around L₂, followed by its reduction to the center manifold. In this reduced dynamics, a convenient Poincaré section shows the interplay of the Lyapunov and halo periodic orbits, Lissajous and quasi-halo tori as well as the stable and unstable manifolds of the planar Lyapunov orbit. To show the effect of the oblateness, the planar Lyapunov family emanating from the Lagrangian points and three-dimensional halo orbits are obtained by the numerical continuation method.     

Autonomous satellite navigation using starlight refraction angle measurements

An on-board autonomous navigation capability is required to reduce the operation costs and enhance the navigation performance of future satellites. Autonomous navigation by stellar refraction is a type of autonomous celestial navigation method that uses high-accuracy star sensors instead of Earth sensors to provide information regarding Earth’s horizon. In previous studies, the refraction apparent height has typically been used for such navigation. However, the apparent height cannot be measured directly by a star sensor and can only be calculated by the refraction angle and an atmospheric refraction model. Therefore, additional errors are introduced by the uncertainty and nonlinearity of atmospheric refraction models, which result in reduced navigation accuracy and reliability. A new navigation method based on the direct measurement of the refraction angle is proposed to solve this problem. Techniques for the determination of the refraction angle are introduced, and a measurement model for the refraction angle is established. The method is tested and validated by simulations. When the starlight refraction height ranges from 20 to 50 km, a positioning accuracy of better than 100 m can be achieved for a low-Earth-orbit (LEO) satellite using the refraction angle, while the positioning accuracy of the traditional method using the apparent height is worse than 500 m under the same conditions. Furthermore, an analysis of the factors that affect navigation accuracy, including the measurement accuracy of the refraction angle, the number of visible refracted stars per orbit and the installation azimuth of star sensor, is presented. This method is highly recommended for small satellites in particular, as no additional hardware besides two star sensors is required.     

CubeSail: A low cost CubeSat based solar sail demonstration mission

CubeSail is a nano-solar sail mission based on the 3U CubeSat standard, which is currently being designed and built at the Surrey Space Centre, University of Surrey. CubeSail will have a total mass of around 3 kg and will deploy a 5 × 5 m sail in low Earth orbit. The primary aim of the mission is to demonstrate the concept of solar sailing and end-of-life de-orbiting using the sail membrane as a drag-sail. The spacecraft will have a compact 3-axis stabilised attitude control system, which uses three magnetic torquers aligned with the spacecraft principle axis as well as a novel two-dimensional translation stage separating the spacecraft bus from the sail. CubeSail’s deployment mechanism consists of four novel booms and four-quadrant sail membranes. The proposed booms are made from tape-spring blades and will deploy the sail membrane from a 2U CubeSat standard structure. This paper presents a systems level overview of the CubeSat mission, focusing on the mission orbit and de-orbiting, in addition to the deployment, attitude control and the satellite bus.     

Spin rate and spin axis orientation of LARES spectrally determined from Satellite Laser Ranging data

Satellite Laser Ranging (SLR) is a powerful technique able to measure spin rate and spin axis orientation of the fully passive, geodetic satellites. This work presents results of the spin determination of LARES – a new satellite for testing General Relativity. 529 SLR passes measured between February 17 and June 9, 2012, were spectrally analyzed. Our results indicate that the initial spin frequency of LARES is f₀ = 86.906 mHz (RMS = 0.539 mHz). A new method for spin axis determination, developed for this analysis, gives orientation of the axis at RA = 12^h22^m48^s (RMS = 49^m), Dec = −70.4° (RMS = 5.2°) (J2000.0 celestial reference frame), and the clockwise (CW) spin direction. The half-life period of the satellite’s spin is 214.924 days and indicates fast slowing down of the spacecraft.     

On the measurements of the moon’s infrared temperature and its relation to the phase angle

Radiometric measurements of the thermal radiation originating from the moon’s surface were obtained using an infrared detector operating at wavelengths between 8 and 14 μm. The measurements cover a full moon cycle. The variation of the moon’s temperature with the lunar phase angle was established. The lunar temperatures were 391 ± 2.0 K for the full moon, 240 ± 3.5 K for the first quarter, and 236 ± 3 K for the last quarter. For the rest of the phase angles, the lunar temperature varied between 170 and 380 K. Our results are comparable with those obtained previously at these phase angles. For the new moon phase, the obtained temperature was between 120 and 133 K. With the exception of the new moon phase, our measurements at all the phase angles were consistent with those obtained using Earth-based data and those obtained by the Diviner experiment and the Clementine spacecraft. At the new phase, our measurements were comparable with those obtained from the ground but were significantly higher than those obtained by the Diviner and Clementine data. We attribute this inconsistency to either the calibration curve of our detector, which does not perform well at very low temperatures, or to infrared emission from the atmosphere. A simple linear model to predict the lunar temperature as a function of the phase angle was proposed. The experimental errors that affect the measured temperatures are discussed.     

Fluctuations of cosmic rays and IMF in the vicinity of interplanetary shocks

Fluctuations of cosmic rays and interplanetary magnetic field upstream of interplanetary shocks are studied using data of ground-based polar neutron monitors as well as measurements of energetic particles and solar wind plasma parameters aboard the ACE spacecraft. It is shown that coherent cosmic ray fluctuations in the energy range from 10 keV to 1 GeV are often observed at the Earth’s orbit before the arrival of interplanetary shocks. This corresponds to an increase of solar wind turbulence level by more than the order of magnitude upstream of the shock. We suggest a scenario where the cosmic ray fluctuation spectrum is modulated by fast magnetosonic waves generated by flux of low-energy cosmic rays which are reflected and/or accelerated by an interplanetary shock.     

Onboard orbit determination using GPS observations based on the unscented Kalman filter

Spaceborne GPS receivers are used for real-time navigation by most low Earth orbit (LEO) satellites. In general, the position and velocity accuracy of GPS navigation solutions without a dynamic filter are 25 m (1σ) and 0.5 m/s (1σ), respectively. However, GPS navigation solutions, which consist of position, velocity, and GPS receiver clock bias, have many abnormal excursions from the normal error range for space operation. These excursions lessen the accuracy of attitude control and onboard time synchronization. In this research, a new onboard orbit determination algorithm designed with the unscented Kalman filter (UKF) was developed to improve the performance. Because the UKF is able to obtain the posterior mean and covariance accurately by using the second-order Taylor series expansion through the sampled sigma points that are propagated by using the true nonlinear system, its performance can be better than that of the extended Kalman filter (EKF), which uses the linearized state transition matrix to predict the covariance. The dynamic models for orbit propagation applied perturbations due to the 40 × 40 geo-potential, the gravity of the Sun and Moon, solar radiation pressure, and atmospheric drag. The 7(8)th-order Runge–Kutta numerical integration was applied for orbit propagation. Two types of observations, navigation solutions and C/A code pseudorange, can be used at the user’s discretion. The performances of the onboard orbit determination were verified using real GPS data of the CHAMP and KOMPSAT-2 satellites. The results of the orbit determination were compared with the precision orbit ephemeris (POE) of the CHAMP and KOMPSAT-2 satellites.     

Alternative transfer to the Earth–Moon Lagrangian points L4 and L5 using lunar gravity assist

Lagrangian points L4 and L5 lie at 60° ahead of and behind the Moon in its orbit with respect to the Earth. Each one of them is a third point of an equilateral triangle with the base of the line defined by those two bodies. These Lagrangian points are stable for the Earth–Moon mass ratio. As so, these Lagrangian points represent remarkable positions to host astronomical observatories or space stations. However, this same distance characteristic may be a challenge for periodic servicing mission. This paper studies elliptic trajectories from an Earth circular parking orbit to reach the Moon’s sphere of influence and apply a swing-by maneuver in order to re-direct the path of a spacecraft to a vicinity of the Lagrangian points L4 and L5. Once the geocentric transfer orbit and the initial impulsive thrust have been determined, the goal is to establish the angle at which the geocentric trajectory crosses the lunar sphere of influence in such a way that when the spacecraft leaves the Moon’s gravitational field, its trajectory and velocity with respect to the Earth change in order to the spacecraft arrives at L4 and L5. In this work, the planar Circular Restricted Three Body Problem approximation is used and in order to avoid solving a two boundary problem, the patched-conic approximation is considered.     

Mars Phobos and Deimos Survey (M-PADS) – A martian Moons orbiter and Phobos lander

We describe a Mars ‘Micro Mission’ for detailed study of the martian satellites Phobos and Deimos. The mission involves two ∼330 kg spacecraft equipped with solar electric propulsion to reach Mars orbit. The two spacecraft are stacked for launch: an orbiter for remote investigation of the moons and in situ studies of their environment in Mars orbit, and another carrying a lander for in situ measurements on the surface of Phobos (or alternatively Deimos). Phobos and Deimos remain only partially studied, and Deimos less well than Phobos. Mars has almost always been the primary mission objective, while the more dedicated Phobos project (1988–89) failed to realise its full potential. Many questions remain concerning the moons’ origins, evolution, physical nature and composition. Current missions, such as Mars Express, are extending our knowledge of Phobos in some areas but largely neglect Deimos. The objectives of M-PADS focus on: origins and evolution, interactions with Mars, volatiles and interiors, surface features, and differences. The consequent measurement requirements imply both landed and remote sensing payloads. M-PADS is expected to accommodate a 60 kg orbital payload and a 16 kg lander payload. M-PADS resulted from a BNSC-funded study carried out in 2003 to define candidate Mars Micro Mission concepts for ESA’s Aurora programme.     

Magnetosphere response to the 2005 and 2006 extreme solar events as observed by the Cluster and Double Star spacecraft

The four identical Cluster spacecraft, launched in 2000, orbit the Earth in a tetrahedral configuration and on a highly eccentric polar orbit (4–19.6 R_E). This allows the crossing of critical layers that develop as a result of the interaction between the solar wind and the Earth’s magnetosphere. Since 2004 the Chinese Double Star TC-1 and TC-2 spacecraft, whose payload comprise also backup models of instruments developed by European scientists for Cluster, provided two additional points of measurement, on a larger scale: the Cluster and Double Star orbits are such that the spacecraft are almost in the same meridian, allowing conjugate studies. The Cluster and Double Star observations during the 2005 and 2006 extreme solar events are presented, showing uncommon plasma parameters values in the near-Earth solar wind and in the magnetosheath. These include solar wind velocities up to ∼900 km s⁻¹ during an ICME shock arrival, accompanied by a sudden increase in the density by a factor of ∼5 and followed by an enrichment in He⁺⁺ in the secondary front of the ICME. In the magnetosheath ion density values as high as 130 cm⁻³ were observed, and the plasma flow velocity there reached values even higher than the typical solar wind velocity. These resulted in unusual dayside magnetosphere compression, detection of penetrating high-energy particles in the magnetotail, and ring current development following several successive injections of energetic particles in the inner magnetosphere, which “washed out” the previously formed nose-like ion structures.     

Generating precise and homogeneous orbits for Jason-1 and Jason-2

Driven by the GMES (Global Monitoring for Environment and Security) and GGOS (Global Geodetic Observing System) initiatives the user community has a strong demand for high-quality altimetry products. In order to derive such high-quality altimetry products, precise orbits for the altimetry satellites are a necessity. With the launch of the TOPEX/Poseidon mission in 1992 a still on-going time series of high-accuracy altimetry measurements of ocean topography started, continued by the altimetry missions Jason-1 in 2001 and Jason-2/OSTM in 2008. This paper contributes to the on-going orbit reprocessing carried out by several groups and presents the efforts of the Navigation Support Office at ESA/ESOC using its NAPEOS software for the generation of precise and homogeneous orbits referring to the same reference frame for the altimetry satellites Jason-1 and Jason-2. Data of all three tracking instruments on-board the satellites (beside the altimeter), i.e. GPS, DORIS, and SLR measurements, were used in a combined data analysis. About 7 years of Jason-1 data and more than 1 year of Jason-2 data were processed. Our processing strategy is close to the GDR-C standards. However, we estimated slightly different scaling factors for the solar radiation pressure model of 0.96 and 0.98 for Jason-1 and Jason-2, respectively. We used 30 s sampled GPS data and introduced 30 s satellite clocks stemming from ESOC’s reprocessing of the combined GPS/GLONASS IGS solution. We present the orbit determination results, focusing on the benefits of adding GPS data to the solution. The fully combined solution was found to give the best orbit results. We reach a post-fit RMS of the GPS phase observation residuals of 6 mm for Jason-1 and 7 mm for Jason-2. The DORIS post-fit residuals clearly benefit from using GPS data in addition, as the DORIS data editing improves. The DORIS observation RMS for the fully combined solution is with 3.5 mm and 3.4 mm, respectively, 0.3 mm better than for the DORIS-SLR solution. Our orbit solution agrees well with external solutions from other analysis centers, as CNES, LCA, and JPL. The orbit differences between our fully combined orbits and the CNES GDR-C orbits are of about 0.8 cm for Jason-1 and at 0.9 cm for Jason-2 in the radial direction. In the cross-track component we observe a clear improvement when adding GPS data to the POD process. The 3D-RMS of the orbit differences reveals a good orbit consistency at 2.7 cm and 2.9 cm for Jason-1 and Jason-2. Our resulting orbit series for both Jason satellites refer to the ITRF2005 reference frame and are provided in sp3 file format on our ftp server.     

空间激光干涉引力波探测器轨道修正方法

针对空间激光干涉引力波探测器轨道修正问题,提出一种基于虚拟编队构型设计的航天器轨道修正方法。空间激光干涉引力波探测器由3颗航天器组成等边三角形构型。由于入轨误差和摄动的影响,探测器的构型不稳定。假设名义轨道上运行着一颗理想航天器,实际轨道上的真实航天器与之组成虚拟编队,探测器的3颗真实航天器分别与对应的理想航天器组成3个虚拟编队。考虑探测器构型稳定性要求和摄动的影响,对虚拟编队的构型进行设计,进而求解航天器平均轨道要素修正量。求解得到的航天器平均轨道要素修正量小于偏差量,轨道修正通过四脉冲控制实现。数值仿真结果表明,该方法通过部分轨道修正满足了探测器的构型稳定性要求,具有减少燃料消耗、延长任务寿命的潜力。      

Precise orbit determination using the batch filter based on particle filtering with genetic resampling approach

In this study, genetic resampling (GRS) approach is utilized for precise orbit determination (POD) using the batch filter based on particle filtering (PF). Two genetic operations, which are arithmetic crossover and residual mutation, are used for GRS of the batch filter based on PF (PF batch filter). For POD, Laser-ranging Precise Orbit Determination System (LPODS) and satellite laser ranging (SLR) observations of the CHAMP satellite are used. Monte Carlo trials for POD are performed by one hundred times. The characteristics of the POD results by PF batch filter with GRS are compared with those of a PF batch filter with minimum residual resampling (MRRS). The post-fit residual, 3D error by external orbit comparison, and POD repeatability are analyzed for orbit quality assessments. The POD results are externally checked by NASA JPL’s orbits using totally different software, measurements, and techniques. For post-fit residuals and 3D errors, both MRRS and GRS give accurate estimation results whose mean root mean square (RMS) values are at a level of 5 cm and 10–13 cm, respectively. The mean radial orbit errors of both methods are at a level of 5 cm. For POD repeatability represented as the standard deviations of post-fit residuals and 3D errors by repetitive PODs, however, GRS yields 25% and 13% more robust estimation results than MRRS for post-fit residual and 3D error, respectively. This study shows that PF batch filter with GRS approach using genetic operations is superior to PF batch filter with MRRS in terms of robustness in POD with SLR observations.     

Coronal radio-sounding detection of a CME during the 1997 Galileo solar conjunction

Frequency fluctuations of the Galileo S-band radio signal were recorded nearly continuously during the spacecraft’s solar conjunction from December 1996 to February 1997. A strong propagating disturbance, most probably associated with a coronal mass ejection (CME), was detected on 7 February when the radio ray path proximate point was on the west solar limb at about 54 solar radii from the Sun. The CME passage through the line of sight is characterized by a significant increase in the fluctuation intensity of the recorded frequency and by an increase in the plasma speed from about 234 km s⁻¹ up to about 755 km s⁻¹. These velocity estimates are obtained from a correlation analysis of frequency fluctuations recorded simultaneously at two widely-separated ground stations. The density turbulence power spectrum is found to steepen behind the CME front. The Galileo radio-sounding data are compared with SOHO/LASCO observations of the CME in the corona and with WIND spacecraft data near the Earth’s orbit.     

Mission feasibility analysis on deflecting Earth-crossing objects using a power limited laser ablating spacecraft

This paper analyzes several mission capabilities to deflect Earth-crossing objects (ECOs) using a conceptual future spacecraft with a power limited laser ablating tool. A constrained optimization problem is formulated based on nonlinear programming with a three-dimensional patched conic method. System dynamics are also established, considering the target ECO’s orbit as being continuously perturbed by limited laser power. The required optimal operating duration and operating angle history of the laser ablating tool are computed for various types of ECOs to avoid an Earth impact. The available final warning time is also determined with a given limited laser power. As a result, detailed laser operating behaviors are presented and discussed, which include characteristics of operating duration and angle variation histories in relation to the operation’s start time and target object’s properties. The calculated durations of the optimal laser operation are also compared to those estimated with first-order approximations previous studies. It is discovered that the duration of the laser operation estimated with first-order approximations could result in up to about 50% error if the operation is started at the final warning time. The laser operation should be started as early as possible because an early start requires a short operating duration with a small operating angle variation. The mission feasibility demonstrated in the present study will give various insights into preparing future deflection missions using power limited spacecraft with a laser ablation tool.     

Why should the latitude of the observer be considered when modeling gradual proton events? An insight using the concept of cobpoint

The shape of flux profiles of gradual solar energetic particle (SEP) events depends on several not well-understood factors, such as the strength of the associated shock, the relative position of the observer in space with respect to the traveling shock, the existence of a background seed particle population, the interplanetary conditions for particle transport, as well as the particle energy. Here, we focus on two of these factors: the influence of the shock strength and the relative position of the observer. We performed a 3D simulation of the propagation of a coronal/interplanetary CME-driven shock in the framework of ideal MHD modeling. We analyze the passage of this shock by nine spacecraft located at ∼0.4 AU (Mercury’s orbit) and at different longitudes and latitudes. We study the evolution of the plasma conditions in the shock front region magnetically connected to each spacecraft, that is the region of the shock front scanned by the “cobpoint” (Heras et al., 1995), as the shock propagates away from the Sun. Particularly, we discuss the influence of the latitude of the observer on the injection rate of shock-accelerated particles and, hence, on the resulting proton flux profiles to be detected by each spacecraft.     

Orbit determination and prediction of GEO satellite of BeiDou during repositioning maneuver

In order to establish a continuous GEO satellite orbit during repositioning maneuvers, a suitable maneuver force model has been established associated with an optimal orbit determination method and strategy. A continuous increasing acceleration is established by constructing a constant force that is equivalent to the pulse force, with the mass of the satellite decreasing throughout maneuver. This acceleration can be added to other accelerations, such as solar radiation, to obtain the continuous acceleration of the satellite. The orbit determination method and strategy are illuminated, with subsequent assessment of the orbit being determined and predicted accordingly. The orbit of the GEO satellite during repositioning maneuver can be determined and predicted by using C-Band pseudo-range observations of the BeiDou GEO satellite with COSPAR ID 2010-001A in 2011 and 2012. The results indicate that observations before maneuver do affect orbit determination and prediction, and should therefore be selected appropriately. A more precise orbit and prediction can be obtained compared to common short arc methods when observations starting 1 day prior the maneuver and 2 h after the maneuver are adopted in POD (Precise Orbit Determination). The achieved URE (User Range Error) under non-consideration of satellite clock errors is better than 2 m within the first 2 h after maneuver, and less than 3 m for further 2 h of orbit prediction.     

Proposal of application of same beam VLBI measurements in precision orbit determination of lunar orbiter and return capsule and lunar gravity field simulation in Chang’E-3 mission

High accuracy differenced phase delay can be obtained by observing multiple point frequencies of two spacecraft using the same beam Very Long Baseline Interferometry (VLBI) technology. Its contribution in lunar spacecraft precision orbit determination has been performed during the Japanese lunar exploration mission SELENE. In consideration that there will be an orbiter and a return capsule flying around the moon during the Chinese lunar exploration future mission Chang’E-3, the contributions of the same beam VLBI in spacecraft precision orbit determination and lunar gravity field solution have been investigated. Our results show that the accuracy of precision orbit determination can be improved more than one order of magnitude after including the same beam VLBI measurements. There are significant improvements in accuracy of low and medium degree coefficients of lunar gravity field model obtained from combination of two way range and Doppler and the same beam VLBI measurements than the one that only uses two way range and Doppler data, and the accuracy of precision orbit determination can reach meter level.     

On the effect of considering more realistic particle shape and mass parameters in MMOD risk assessments

One of the primary mission risks tracked in the development of all spacecraft is that due to micro-meteoroids and orbital debris (MMOD). Both types of particles, especially those larger than 0.1 mm in diameter, contain sufficient kinetic energy due to their combined mass and velocities to cause serious damage to crew members and spacecraft. The process used to assess MMOD risk consists of three elements: environment, damage prediction, and damage tolerance. Orbital debris risk assessments for the Orion vehicle, as well as the Shuttle, Space Station and other satellites use ballistic limit equations (BLEs) that have been developed using high speed impact test data and results from numerical simulations that have used spherical projectiles. However, spheres are not expected to be a common shape for orbital debris; rather, orbital debris fragments might be better represented by other regular or irregular solids. In this paper we examine the general construction of NASA’s current orbital debris (OD) model, explore the potential variations in orbital debris mass and shape that are possible when using particle characteristic length to define particle size (instead of assuming spherical particles), and, considering specifically the Orion vehicle, perform an orbital debris risk sensitivity study taking into account variations in particle mass and shape as noted above. While the results of the work performed for this study are preliminary, they do show that continuing to use aluminum spheres in spacecraft risk assessments could result in an over-design of its MMOD protection systems. In such a case, the spacecraft could be heavier than needed, could cost more than needed, and could cost more to put into orbit than needed. The results obtained in this study also show the need to incorporate effects of mass and shape in mission risk assessment prior to first flight of any spacecraft as well as the need to continue to develop/refine BLEs so that they more accurately reflect the shape and material density variations inherent to the actual debris environment.